Primer-Field Complete Functions and Factoring Polynomials over Finite Fields

Abstract

We relate the arithmetic straight-line complexity over a field GF(p) (p is a prime) of the parity function lp to the Boolean complexity of the problem of factoring polynomials over finite fields of characteristic p. A procedure is described which converts an arithmetic straight-line program for lp into a factoring algorithm.  As a consequence, a short straight-line program for lp would imply the existence of an efficient factoring method.